Building probabilistic three-dimensional models (P3DMs) from satellite imagery requires extremely accurate camera data. Commercial and National Technical Means imagery has a well defined camera model in the National Imagery Transmission Format (NITF) header that contains Rational Polynomial Coefficient (RPC) pointing data. This RPC data aids in back projecting 2-dimensional (2D) pixel data into 3-dimensional (3D) space. However, all RPC camera data has some amount of uncertainty associated with them. For example, Digital Globe's Quickbird satellite advertises a 23 meter circular error and 17 meter linear error of [1]. In order to build an accurate P3DM, camera pose data must be accurate to the lowest level of a volume element or “voxel” represented in the model. For example, if the voxels in the P3DM are each 1 meter in size, the pointing accuracy must be at least 1 meter.
P3DMs have been successfully demonstrated to correct satellite RPC pointing errors. The state of the art technique is described in [2]. In [2], the authors describe an approach to correct satellite pointing errors by using probabilistic three dimensional edge models (3D edge models) combined with and a block adjustment algorithm. 3D edge models are distinct from P3DMs in that they only contain probabilistic edge elements in volumetric space as opposed to the appearance and surface geometry data found in full P3DMs. The procedure begins by using 5 precisely registered satellite images taken from a diverse set of collection geometries to create a 3D edge model. Since it is grounded in true geo-coordinates, once created, the 3D edge model can be rendered from any arbitrary viewing angle. Given a 3D edge model and a new satellite image with RPCs, the 3D edge model can be projected and rendered into the same camera frame as the new image. From there, assuming a high-quality 3D edge model, the satellite image simply needs to be block adjusted using a procedure, such as that described in [3] to correct the pointing error.
The authors of [2] corrected a set of training images using a manually selected tie-point across the set of images. This manual correction step is required since, as noted above, all satellite images have some level of pointing uncertainty in the RPC data. Without this step, the pointing errors would be too great to allow the 3D model to converge accurately. However, for satellite systems with very complex and diverse viewing parameters (i.e. illumination, geometry, etc), the number of accurate camera models needs to be drastically increased. Experiments with P3DM on National Geospatial-Intelligence Agency (NGA) imagery, for example, indicates that as many as 10-20 images may be required depending on the area of interest.
Alternatively, the authors of [4] used a high-resolution Light Detection and Ranging (LiDAR) Digital Elevation Model (DEM) to seed their 3D edge model instead of a set of manually adjusted images. This technique has proven successful for those limited areas of interest where a high quality LiDAR DEM is available.
The use of manually corrected imagery or a LiDAR DEM is often referred to as “bootstrapping” a 3D edge model. The aforementioned techniques have their limitations. For example, manually correcting imagery camera models can be time consuming and requires a certain amount of training to perform. LiDAR is not available for modeling denied areas. Without a set of manually corrected images or a LiDAR DEM, there is currently no technique to automatically build P3DMs and use the built P3DMs to correct satellite pointing errors.